In a large bowl beat butter and peanut butter with an electric mixer on medium to high speed for 30 seconds. Add the brown sugar, vanilla, and salt. Beat until mixture is combined, scraping sides of bowl occasionally. Beat in the oat flour, rolled oats, and coconut flour. Stir in miniature chocolate pieces.
Flatten dough between two sheets of waxed paper to about 3/4-inch thick. Cut small footballs out of the dough using a 2 1/4-inch football-shape cutter. Reroll and repeat with remaining dough. Dip pop stick in melted chocolate and insert pop sticks into footballs, if desired. Chill cut outs for 20 minutes.
Dip dough into chocolate and transfer to a waxed paper-lined baking pan until set. Pipe football laces on chocolate with melted white chocolate.